Peel potatoes and square off sides and ends. Cut peeled potatoes into 10 to 12 large wedges per potato. Place in a large bowl and add cold water to cover by 1 inch, then let soak in the refrigerator at least 4 hours or up to 24 hours. Drain potatoes and spread on a clean kitchen towel and dry completely, patting off as much water as possible.
Line baking sheets with a double thickness of paper towels. Heat 2 inches of oil in a heavy stockpot over medium heat to 300 degrees on a deep-fry thermometer. Working in batches and using a spider, lower potatoes into the oil (the temperature will drop significantly, to about 270 degrees, and slowly climb up again) and stir to separate. Cook just until softened (test one by breaking it in half; it should be almost completely cooked through), but not brown, about 3 minutes. Use a spider or slotted spoon to transfer to one of the prepared baking sheets to drain, spreading in a single layer. Allow oil to return to 300 degrees between each batch. (The potatoes can be blanched and left to drain on the prepared baking sheets for 4 hours in the refrigerator before finishing, replacing the paper towels as necessary.)
Heat oil to 350 degrees.
Again working in batches, add blanched potatoes to oil (the temperature will drop to about 340 degrees) and stir to separate. Cook until golden brown, 4 to 4 1/2 minutes. Use a spider or slotted spoon to transfer to prepared baking sheets to drain (replace paper towels if you are using the same baking sheets as above). Allow oil to return to 350 degrees between each batch.
Sprinkle with salt and serve immediately.